Question

The relationship between γd, G, w and S is_______

(a) γd = G γw*(1+(\(\frac{wG}{S}\)))

(b) γd = G γw – (1+(\(\frac{wG}{S}\)))

(c) γd = G γw/(1+(\(\frac{wG}{S}\)))

(d) γd = G γw+(1+(\(\frac{wG}{S}\)))

This question was posed to me in a national level competition.

The doubt is from Functional Relationships topic in section Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Right answer is (c) γd = G γw/(1+(\(\frac{wG}{S}\)))

To explain I would say: The dry unit weight is given by,

γd = \(\frac{Gγ_w}{(1+e)}\)

but e=\(\frac{wG}{S}\)

substituting e in  γd

 ∴ γd = G γw/(1+(\(\frac{wG}{S}\))).